Sluggish Private Investment in Japan s Lost Decade: Mixed Frequency Vector Autoregression Approach

Transcription

1 Sluggish Private Investment in Japan s Lost Decade: Mixed Frequency Vector Autoregression Approach Kaiji Motegi Akira Sadahiro Kobe University Waseda University This Draft: June 19, 17 Abstract It is well known that sluggish private investment plagued the Japanese macroeconomy during the Lost Decade. Previous empirical papers have not reached a clear consensus on what caused the investment slowdown. This paper sheds new light on this issue by fitting a mixed frequency vector autoregressive model to monthly stock prices, quarterly bank loans, firm profit, and private investment. Monthly stock prices explain as much as 5.7% of the long-run forecast error variance of investment. Moreover, we reveal a spiral of declining stock prices, profit, and investment. Finally, the stagnation of bank loans is a consequence of declined stock prices, and it is not a cause of declined investment. Keywords: Japan s Lost Decade, Mixed Data Sampling (MIDAS), mixed frequency vector autoregression (MF-VAR), private investment. JEL Classification: C3, E, E. We thank Shigeyuki Hamori, Stephen Raymond, and Forrest Spence for valuable comments. We also thank participants of the nd Kansai Keiryo Keizaigaku Kenkyukai, 6th Seminar on Time Series and Financial Engineering, and the 15 Spring Meeting of Japanese Economic Association for helpful comments. The first author is grateful for financial supports of JSPS KAKENHI (Grant Number: 16K171). Corresponding author. Graduate School of Economics, Kobe University. -1 Rokkodai-cho, Nada, Kobe, Hyogo Japan. motegi@econ.kobe-u.ac.jp Professor Emeritus, Waseda University Nishi-Waseda, Shinjuku, Tokyo Japan. E- mail: sadahiro@waseda.jp

2 1 Introduction Japan experienced more than a decade of economic stagnation, which is called the Lost Decade or sometimes the Lost Two Decades, after the stock market bubble burst in 199. It is well known that the slump of private non-residential investment plagued the Japanese economy in that period. Macroeconomists tried to explain what caused the investment slump, ending up with mixed results. Was the sluggish investment caused by firm-specific factors, bank-specific factors, or some other macroeconomic factors affecting both firms and banks? Firm-specific factors include a decrease in current or expected future profit that discourages firms from investing. Bank-specific factors, also called credit crunch, include a tougher lending attitude of banks due to their worse financial conditions. Typically, previous researchers test for the relevance of bank-specific factors in two steps. First, they investigate the impact of banks financial conditions on their attitude to lend money to private firms. Second, researchers estimate the sensitivity of corporate investment functions to the lending attitude of banks. For the first step, most researchers have found a significant impact of banks financial conditions on their lending attitude in , when Japanese banks were facing particularly serious situations. Empirical results for other periods are mixed, however. Ito and Sasaki () and Dell Ariccia (3) argue that declined bank lending in the early 199s and early s was indeed caused by banks financial conditions. Horiuchi and Shimizu (1998) and Woo (3), in contrast, find that the worse financial conditions of banks did not cause less bank lending in early 199s. For the second step, Motonishi and Yoshikawa (1999) find that the investment slump in was likely attributable to the tougher sentiment of money lenders, a supportive evidence for the bank-specific factor. Ogawa (3) obtains similar results for each year of Hayashi and Prescott (), in contrast, argue that the declined bank lending did not have a significant impact on investment, since firms could have financed investment by liquidating their own land or financial assets. 1 There exists another approach that investigates a dynamic interrelationship between bank-specific factors and firm-specific factors, using vector autoregression (VAR). Sadahiro (5) finds that the investment slump during the Lost Decade was Granger-caused by a decrease in firm profit and not by bank loans. He therefore claims that a firm-specific 1 Gibson (1995) shows that the investment of private firms is significantly affected by the financial condition of their main banks in Gibson (1997), however, finds a weaker evidence for See Miyao (6, Sec. 8.) for more detailed literature review on the relationship between bank loans and investment. 1

3 factor better accounts for the sluggish private investment than a bank-specific factor. 3 From a methodological point of view, previous papers share a common issue of temporal aggregation. Key variables in this field (e.g. private non-residential investment, firm-specific bank lending for investment, and firm profit) are sampled quarterly or even less frequently. Previous papers were forced to aggregate high frequency variables, such as stock prices and interest rates, since classical models require all variables to have a single frequency. Temporal aggregation is known to have an adverse impact on statistical inference. The present paper sheds new light on the literature by exploiting mixed frequency data. Analysis of mixed frequency data, called Mixed Data Sampling (MIDAS) regression, was explored by Ghysels, Santa-Clara, and Valkanov (), Ghysels, Santa-Clara, and Valkanov (6), and Andreou, Ghysels, and Kourtellos (1). 5 In particular, Ghysels, Santa-Clara, and Valkanov () demonstrate that MIDAS regressions lead to more efficient estimation than the classical approach of aggregating all series to the least frequency sampling. VAR models for mixed frequency data were independently introduced by McCracken, Owyang, and Sekhposyan (15), Anderson, Deistler, Felsenstein, Funovits, Koelbl, and Zamani (16), and Ghysels (16). 6 Ghysels (16) mixed frequency VAR (henceforth MF-VAR) is a user-friendly model that does not require any filtering procedure. A major advantage of MF-VAR relative to single-frequency VAR is that high frequency variables are allowed to have heterogeneous impacts on a low frequency variable within each low frequency time period. 7 Not many applied papers use MF-VAR so far, since it is a relatively new tool. We are not aware of any applied paper that analyzes the Japanese economy based on MF-VAR. This paper fills that gap by analyzing the interaction of monthly stock prices, quarterly bank loans, firm profit, and private investment. Stock prices have a close connection with Tobin s Q, one of the most well-known factors associated with private investment. 8 Computation of Tobin s Q requires corporate net worth data, which are sampled at a quarterly or less frequently level. Stock prices, in contrast, are sampled at much higher frequency than a quarterly level (e.g. monthly, daily, or even intradaily). We compare 3 Mizobata (15) fits a panel VAR for investment, hiring, and financial indicators of Japanese firms. Silvestrini and Veredas (8) survey the effects of temporal aggregation on time series models. 5 See Armesto, Engemann, and Owyang (1) and Andreou, Ghysels, and Kourtellos (11) for surveys. 6 Foroni, Ghysels, and Marcellino (13) survey mixed frequency VAR models and related literature. 7 Ghysels, Hill, and Motegi (16) elaborate the statistical properties of MF-VAR, with a particular focus on Granger causality. 8 See Hayashi (198), Fazzari, Hubbard, and Petersen (1988), and Abel and Eberly (199) for early contributions to Tobin s Q-theory. Fore more recent work, see Mizobata (1) and references therein.

4 a model with quarterly stock prices and a model with monthly stock prices in order to highlight that changing the sampling frequency can alter empirical results considerably. Our empirical findings are summarized as follows. First, monthly stock prices explain as much as 5.7% of the forecast error variance of private investment in a long-run (i.e. h = 1 quarters). Second, based on impulse response analysis, we reveal a spiral of declining stock prices, firm profit, and investment. Lower stock prices affected firm profit negatively, which discouraged firms investment. The investment slowdown put a further downward pressure on the stock prices, creating a loop of negative feedback effects. Third, the stagnation of bank lending is a consequence of a decrease in stock prices, and it is not a cause of a decrease in investment. The long-run forecast error variance of bank lending is explained 1.% by stock prices. Bank lending, by contrast, has only negligible impacts on stock prices, profit, and investment. Thus, the firm-specific factor (i.e. firm profit) better explains the sluggish investment than the bank-specific factor (i.e. bank lending). We would need to use quarterly stock prices if we were forced to work with singlefrequency data. Aggregating monthly stock prices into a quarterly level underestimates the influence of stock prices. Quarterly stock prices explain 31.8% of the long-run forecast error variance of investment (as opposed to 5.7% in the mixed frequency case). Also, aggregating stock prices weakens the statistical significance of the spiral of stock prices, firm profit, and investment. The impulse response of stock prices to investment is not significant at the 5% level when aggregating the stock prices. The mixed frequency approach therefore yields richer economic insights than the classical approach. The remainder of the paper is organized as follows. In Section we describe the MF-VAR methodology. In Section 3 we explain our data and perform some preliminary analysis. In Section we present main empirical results. Section 5 concludes the paper. Methodology We begin with a single-frequency VAR and then proceed to a mixed frequency VAR in order to show that the choice of sampling frequency can change empirical results considerably..1 Quarterly VAR Let t {1,..., n} signify each quarter. Let SP Q t be a stock price index. Superscript Q is put in order to distinguish a quarterly level from a monthly level explicitly. Let BL t be 3

5 bank lending to private firms; let π t be firm profit; let I t be private investment. Assume that each series is sufficiently differenced so that the covariance stationarity is satisfied. See Section 3. for detailed discussions of data handling. As a benchmark, formulate a quarterly VAR() model: SP Q t BL t π t = I t a 11,k a 1,k a 13,k a 1,k SP Q a 1,k a,k a 3,k a,k a 31,k a 3,k a 33,k a 3,k π t a 1,k a,k a 3,k a,k I t k k=1 t k BL t k + ϵ 1t ϵ t ϵ 3t ϵ t. (1) Lag length is set to be quarters so that we can capture potential seasonality. A constant term is omitted to save the number of parameters. We demean each series before fitting the model.. Mixed Frequency VAR We now formulate Ghysels (16) MF-VAR consisting of monthly stock prices and quarterly BL, π, and I. While one could be tempted to choose a weekly or daily level instead of the monthly level, MF-VAR is primarily designed for a small ratio of sampling frequencies. 9 To express monthly stock prices, let SP jt denote a stock price at the j-th month of quarter t, where j {1,, 3}. For example, if t signifies the first quarter of, then SP 1t corresponds to January ; SP t to February ; SP 3t to March ; SP 1t+1 to April, etc. The quarterly stock price SP Q t is interpreted as SP Q t = SP jt. () To avoid notational confusion, we distinguish monthly stock prices {SP 1, SP, SP 3 }, quarterly stock prices SP Q, and a general notion of stock prices SP hereafter. j=1 9 Addressing a large ratio of sampling frequencies is an ongoing issue that involves dimension-reduction techniques. See Götz, Hecq, and Smeekes (16) and Ghysels, Hill, and Motegi (17) for early contributions.

6 The MF-VAR() model is specified as SP 1t SP t SP 3t = BL t π t I t } {{ } =X t or compactly a 11,k a 1,k a 13,k a 1,k a 15,k a 16,k SP 1,t k a 1,k a,k a 3,k a,k a 5,k a 6,k SP,t k a 31,k a 3,k a 33,k a 3,k a 35,k a 36,k SP 3,t k a 1,k a,k a 3,k a,k a 5,k a 6,k BL t k a 51,k a 5,k a 53,k a 5,k a 55,k a 56,k π t k a 61,k } a 6,k a 63,k a 6,k {{ a 65,k a 66,k }} I t k {{ } =A k =X t k k=1 X t = + ϵ 1t ϵ t ϵ 3t ϵ t ϵ 5t ϵ 6t }{{} =ϵ t, (3) A k X t k + ϵ t. () k=1 Lag length is set to be quarters for a fair comparison with the quarterly model (1). 1 A key feature of (3) is that SP 1t, SP t, and SP 3t are stacked in a vector. To see an advantage of this approach, pick the last row of (3): I t = [ 3 ] a 6j,k SP j,t k + a 6,k BL t k + a 65,k π t k + a 66,k I t k + ϵ 6t. k=1 j=1 Since a 61,k, a 6,k, and a 63,k can take different values from each other, SP 1,t k, SP,t k, and SP 3,t k are allowed to have heterogeneous impacts on I t. Recall from (1) and () that the quarterly model implies that I t = k=1 [a 1,k ( 1 3 ) ] 3 SP j,t k + a,k BL t k + a 3,k π t k + a,k I t k + ϵ t. (5) j=1 Equation (5) assumes implicitly that SP 1,t k, SP,t k, and SP 3,t k have a homogeneous impact of a 1,k /3 on I t. That feature rules out the possibility of seasonal effects and lagged information transmission within each quarter. MF-VAR is more flexible than the quarterly VAR in that regard. In terms of asymptotic theory, MF-VAR can be treated in the same way as classical VAR note that MF-VAR model () has an identical appearance with a standard VAR with six variables. Standard regularity conditions therefore all carry over. First, we assume that all roots of the polynomial det(i 6 k=1 A kz k ) = lie outside the unit circle, where det( ) means the determinant. Second, {ϵ t } is a strictly stationary martingale 1 Model () is a reduced-form model. We are not aware of any applied paper with a structural form of Ghysels (16) MF-VAR, and that seems to be an interesting future task. In this paper we focus on reduced form to see how empirical results change by switching from single-frequency VAR to MF-VAR. 5

7 Â k. 11 We perform impulse response analysis and forecast error variance decomposition for difference sequence with finite second moment. Third, {X t, ϵ t } obey α-mixing. These assumptions ensure the consistency and asymptotic normality of least squares estimator each model. They require a choice of the Cholesky order. We set SP Q BL π I for the quarterly model; SP 1 SP SP 3 BL π I for the mixed frequency model. These orders are in line with actual announcement schedules in Japan. See Section 3.1 for more details. 3 Data and Preliminary Statistics In this section we explain how our data are retrieved and transformed, and perform some preliminary analysis. 3.1 Data Source For stock prices, we retrieve a monthly average of daily closing prices of Nikkei Stock Average from Federal Reserve Economic Data. For firm profit, we use Ordinary Profits, All Industries within Financial Statements Statistics of Corporations by Industry published quarterly by the Ministry of Finance, Japan. Private non-residential investment, our main objective, is proxied by Nominal Private Non-Residential Investment of the System of National Accounts (93SNA), published quarterly by the Economic and Social Research Institute, Cabinet Office. We use figures from annual revisions (as opposed to preliminary estimates). Bank loan data are less straightforward to organize. Our primary source is Loans and Bills Discounted by Sector (by Type of Major Industries) published quarterly by the Bank of Japan. Since we are interested in loans for investment, we focus on a component called Loans for Fixed Investment. It consists of Banking Accounts/Domestically Licensed Banks and Trusts Accounts/Domestically Licensed Banks. For each account we subtract loans to Local Governments and Households from loans to Total Including Others, since we are interested in private non-residential investment. We then sum up the two accounts. The resulting series, which we will analyze hereafter, represents firm-specific bank loans for private investment See Ghysels, Hill, and Motegi (16) for complete details. 1 The Bank of Japan also publishes Deposits, Vault Cash, and Loans and Bills Discounted, in which monthly data of firm-specific bank loans for private investment are available. That series, however, is not suitable for the analysis of the Lost Decade since it only dates back to April

8 As stated in Section, we use the Cholesky decomposition with order SP BL π I when performing impulse response analysis and variance decomposition. This order is in line with actual publication schedules in Japan. Stock prices SP are observed almost instantaneously. Bank loans BL are observed roughly in two months and fifteen days (e.g. bank loans for the first quarter of, written as Q1, were announced in the middle of May ). Firm profit π is observed roughly in three months and a few days (e.g. firm profit for Q1 was announced in early June ). Investment I comes last since our figures are based on annual revisions, which take at least three quarters. Investment data for 1999Q-Q1 were revised in December ; investment data for Q-1Q1 were revised in December 1, etc. 3. Preliminary Sample Statistics Our sample period covers months (68 quarters) between January 199 and December 6. There is a broad consensus that the Lost Decade was triggered by the stock market bubble burst in early 199. It is thus reasonable to start our sample period at 199Q1. We choose 6Q as the end of our sample period, based on the trend of bank lending. The outstanding of bank loans was growing at about 15% from previous year in early 199. The growth rate kept slowing down to hit % in 199 and then remained negative for about 1 consecutive years. Bank loans finally began increasing in late 6, a symbolic phenomenon suggesting the end of the Lost Decade. Based on Phillips and Perron s (1988) unit root test with and without a time trend, we decided to take the first difference for {SP, π, I} and the second difference for BL in order to ensure stationarity. For the former, we compute 1 times year-to-year log difference of the level series. For the latter, we compute changes in 1 times year-to-year log difference of the outstanding of the bank loans. We took the year-to-year difference in order to eliminate potential seasonality. In Table 1, we report the result of the Phillips-Perron tests for the sufficiently differenced versions of {SP 1, SP, SP 3, SP Q, BL, π, I}. We consider two specifications for the test equation. In the first case, an intercept is included and a trend is not included. In the second case, both intercept and trend are included. Bartlet kernel with the Neweyand-West automatic bandwidth selection is used for each case. Insert Table 1 here. When the test equation has an intercept only, the null hypothesis of unit root is rejected at the 1% level for investment and 5% level for all other series. When the test 7

9 equation has both intercept and trend, the null hypothesis is not rejected at the 1% level for investment with p-value.15; it is rejected at the 1% level for SP Q and π; it is rejected at the 5% level for all other series. The results for investment are mixed, but we assume that stationarity is satisfied in view of the test result without a trend. In Figure 1 we present time series plots of the sufficiently differenced series. From a visual inspection, we observe a positive correlation between stock prices and firm profit. These series seem to be followed by private investment. We thus expect that stock prices and profit should be relevant factors that predict investment. It is not clear from Figure 1 how bank loans are affecting or affected by other series. Insert Figure 1 here. Table reports sample statistics of the differenced series. SP 1, SP, and SP 3 have some interesting differences. First, their median is %, -7.31%, and -5.3% respectively. SP has worse performance by.1% points than SP 3. Second, SP 3 has weaker asymmetry than SP 1 and SP in terms of skewness. The heterogeneous characteristics of SP 1, SP, and SP 3 suggest a potential benefit of the MF-VAR. Insert Table here. The Kolmogorov-Smirnov test rejects the null hypothesis of normality for bank loans at the 1% level. The Anderson-Darling test rejects the null hypothesis of normality for bank loans at 1%, investment at 5%, and profit at 1%. Hence these series (especially bank loans) likely have non-normal distributions. As demonstrated in Ghysels, Hill, and Motegi (16), the asymptotic theory of (MF-)VAR models does not require the normality assumption. Contemporaneous and lagged correlation coefficients between each pair of variables confirm the visual lead/lag relationships observed in Figure between SP Q t First, the correlation and π t is fairly large at.58. We get similar results after replacing SP Q t are peaked at with SP 1t, SP t, or SP 3t. Second, the correlations between I t and SP Q t k the fourth lag with.311,.37,.53,.589, and.5 for k = 1,..., 5. Replacing SP Q t k with SP 1,t k, SP,t k, or SP 3,t k yields similar results. Third, the correlations between I t and π t k are peaked at the second lag with.65,.761, and.73 for k = 1,, Tables or figures of correlations are omitted for brevity but available upon request. 8

10 Empirical Results This section reports our empirical results for the quarterly and mixed frequency VAR models..1 Quarterly VAR We first discuss the quarterly VAR model. See Figure for impulse response functions (IRFs) with 95% confidence intervals. The confidence intervals are constructed by parametric bootstrap for each horizon h =, 1,..., 1, using the least squares estimator Âk, error covariance estimator ˆΩ = (1/n) n t=1 ˆϵ tˆϵ t, and normal random numbers. The number of bootstrap samples is 1,. Insert Figure here. First, the IRF of private investment I to a 1σ shock in stock prices SP Q, written as SP Q I, is significantly positive at horizons h =, 5, 6, 7. This result is consistent with the fact that the correlation coefficient between I t and SP Q t k reaches a peak of.589 when k =. Second, π I is significantly positive at h =,, 3. This result is again consistent with the fact that the correlation between I t and π t k reaches a peak of.761 when k =. Third, BL I is clearly insignificant at any horizon, a strong evidence against the bank-specific factor. Hence, stock prices and firm profit are likely primary drivers of private investment. In Table 3, the forecast error variance decomposition of investment confirms the large explanatory power of stock prices and profit and the small explanatory power of bank loans. In the long-run h = 1, the forecast error variance of I is explained 31.8% by SP Q, 6.3% by BL, 5.5% by π, and 36.% by I itself. Insert Table 3 here. The quarterly VAR exhibits a relatively weak degree of interdependence. Table 3 indicates that 8.7% of the long-run forecast error variance of SP Q, 7.7% of BL, 5.6% of π, and 36.% of I are explained by themselves. In particular, it is somewhat unsatisfactory that the model explains only = 63.6% of our main target I. Also, the IRFs of SP Q to BL, π, and I are all insignificant at any horizon (Panels 1-3 of Figure ). 9

11 . Mixed Frequency VAR We now discuss the MF-VAR model. See Figure 3.A-3.C for IRFs. Figure 3.A shows IRFs of SP to other variables; Figure 3.B shows IRFs of {BL, π, I} to SP ; Figure 3.C shows IRFs not involving SP. Insert Figures 3.A-3.C here. We first focus on how our main target I is explained in MF-VAR. In Figure 3.C, π I is significantly positive at h =, 1,, 3, again suggesting the relevance of the firm-specific factor. Also, SP 1 I is significantly positive at h = 5, 6, 7; SP 3 I is significantly positive at h = (Figure 3.B). Finally, BL I is far from significant at any horizon, a strong evidence against the bank-specific factor (Figure 3.C). These results are consistent with the quarterly model, and also with Sadahiro (5), who finds that the firm-specific factor outweighs the bank-specific factor. The MF-VAR achieves greater explanatory power on investment than the quarterly VAR. In Table, the long-run forecast error variance of I is attributed to SP 1 by.6%, SP by 18.%, SP 3 by 9.9%, BL by.%, π by.%, and I itself by.9%. The total contribution of stock prices is as large as = 5.7% as opposed to 31.8% in the quarterly VAR. It suggests that aggregating monthly stock prices into a quarterly level underestimates the influence of stock prices. Insert Table here. We next discuss an overall interaction in the entire model. In view of Table, the MF-VAR accounts for 5.3% of the long-run forecast error variance of BL, 7.% of π, and 75.1% of I, net of their own contributions. Recall from Table 3 that the portion was 9.3% for BL, 5.% for π, and 63.6% for I in the quarterly VAR. Hence the mixed frequency approach delivers a tighter interdependence than the quarterly approach. Impulse responses in the MF-VAR also provide richer implications than in the quarterly VAR. Recall from Figure that five pairs have significant IRFs in the quarterly VAR: SP Q BL, SP Q π, BL π, SP Q I, and π I. In view of Figures 3.A-3.C, the MF-VAR preserves all those patterns except for BL π, which was only marginally significant in the quarterly VAR. (SP Q is now replaced with SP 1, SP, or SP 3.) Besides those pairs, the MF-VAR produces three more cases of significant IRFs: I SP 1 at h = 1, 3; I SP at h = 3; I SP 3 at h =. These extra results imply that each of SP, BL, π, and I is significantly explained by at least one variable. 1

12 To summarize the impulse response analysis, the MF-VAR provides an interesting picture on how investment and other variables interact to each other. There is a spiral that SP π I SP. A decrease in stock prices lowered the firm profit, which discouraged firms from investing. The declined investment put a further downward pressure on the stock prices, creating a loop of negative feedback effects. Note that the spiral SP π I SP is less apparent in the quarterly VAR, since the IRF of SP Q to I is not significant at the 5% level (Panel 3, Figure ). The mixed frequency approach therefore yields richer economic insights than the single-frequency approach. Finally, both approaches indicate that a decrease in bank loans is a consequence of a decrease in stock prices, and it is not a cause of the declined investment. We thus conclude that the firm-specific factor outweighs the bank-specific factor in terms of explaining the investment stagnation. 5 Conclusions This paper reconsiders the sluggish private investment in Japan s Lost Decade, using a recent tool of MF-VAR. Our model consists of monthly stock prices SP, quarterly bank loans BL, firm profit π, and investment I. The classical VAR aggregates the monthly stock prices into a quarterly level. An advantage of MF-VAR is that monthly stock prices are allowed to have heterogeneous impacts on the other quarterly series. Our empirical results are summarized as follows. First, monthly stock prices account for as much as 5.7% of the long-run forecast error variance of private investment. Second, we have revealed a spiral that SP π I SP. Third, a decrease in bank loans is a consequence of a decrease in stock prices, and it is not a cause of the declined investment. We therefore conclude that the firm-specific factor (i.e. firm profit) better explains the sluggish investment than the bank-specific factor (i.e. bank lending). Aggregating monthly stock prices into a quarterly level underestimates the influence of stock prices. Quarterly stock prices explain 31.8% of the long-run forecast error variance of investment (as opposed to 5.7% in the MF-VAR). Also, the temporal aggregation of stock prices makes the spiral SP π I SP less apparent due to the insignificant impulse response of SP to I. Overall, the mixed frequency approach yields richer economic insights than the single-frequency approach. References Abel, A. B., and J. C. Eberly (199): A Unified Model of Investment under Uncertainty, American Economic Review, 8,

13 Anderson, B. D. O., M. Deistler, E. Felsenstein, B. Funovits, L. Koelbl, and M. Zamani (16): Multivariate AR Systems and Mixed Frequency Data: G- Identifiability and Estimation, Econometric Theory, 3, Andreou, E., E. Ghysels, and A. Kourtellos (1): Regression Models with Mixed Sampling Frequencies, Journal of Econometrics, 158, (11): Forecasting with Mixed-Frequency Data, in Oxford Handbook of Economic Forecasting, ed. by M. Clements, and D. Hendry, pp Armesto, M., K. Engemann, and M. Owyang (1): Forecasting with Mixed Frequencies, Federal Reserve Bank of St. Louis Review, 9, Dell Ariccia, G. (3): Banks and Credit in Japan, in Japan s Lost Decade: Policies for Economic Revival, ed. by T. Callen, and J. D. Ostry, pp Washington, D.C.: International Monetary Fund. Fazzari, S. M., R. G. Hubbard, and B. C. Petersen (1988): Financing Constraints and Corporate Investment, Brookings Papers on Economic Activity, 1, Foroni, C., E. Ghysels, and M. Marcellino (13): Mixed-Frequency Vector Autoregressive Models, in VAR Models in Macroeconomics New Developments and Applications: Essays in Honor of Christopher A. Sims, ed. by T. B. Fomby, L. Kilian, and A. Murphy, vol. 3, pp Emerald Group Publishing Limited. Ghysels, E. (16): Macroeconomics and the Reality of Mixed Frequency Data, Journal of Econometrics, 193, Ghysels, E., J. B. Hill, and K. Motegi (16): Testing for Granger Causality with Mixed Frequency Data, Journal of Econometrics, 19, 7 3. (17): Testing a Large Set of Zero Restrictions in Regression Models, with an Application to Mixed Frequency Granger Causality, Working paper, University of North Carolina at Chapel Hill and Kobe University. Ghysels, E., P. Santa-Clara, and R. Valkanov (): The MIDAS Touch: Mixed Data Sampling Regression Models, Working Paper, UCLA and UNC. (6): Predicting volatility: Getting the Most out of Return Data Sampled at Different Frequencies, Journal of Econometrics, 131, Gibson, M. S. (1995): Can Bank Health Affect Investment? Evidence from Japan, Journal of Business, 68, (1997): More Evidence on the Link between Bank Health and Investment in Japan, Journal of the Japanese and International Economies, 11, Götz, T., A. Hecq, and S. Smeekes (16): Testing for Granger Causality in Large Mixed-Frequency VARs, Journal of Econometrics, 193,

14 Hayashi, F. (198): Tobin s Marginal q and Average q: A Neoclassical Interpretation, Econometrica, 5, 13. Hayashi, F., and E. C. Prescott (): The 199s in Japan: A Lost Decade, Review of Economic Dynamics, 5, Horiuchi, A., and K. Shimizu (1998): The Deterioration of Bank Balance Sheets in Japan: Risk-Taking and Recapitalization, Pacific-Basin Finance Journal, 6, 1 6. Ito, T., and Y. N. Sasaki (): Impacts of the Basle Capital Standard on Japanese Banks Behavior, Journal of the Japanese and International Economies, 16, McCracken, M. W., M. Owyang, and T. Sekhposyan (15): Real-Time Forecasting with a Large, Mixed Frequency, Bayesian VAR, No. 15-3, FRB St Louis Paper. Miyao, R. (6): Makuro Kinyu Seisaku no Jikeiretsu Bunseki. Tokyo: Nikkei, Inc. Mizobata, H. (1): What Determines the Japanese Firm Investments: Real or Financial?, Applied Economics, 6, (15): Hiring, Investments, and Financial Distress: Evidence from a Panel VAR Analysis of Japanese Firms, Economics Bulletin, 35, Motonishi, T., and H. Yoshikawa (1999): Causes of the Long Stagnation of Japan during the 199s: Financial or Real?, Journal of the Japanese and International Economies, 13, 181. Ogawa, K. (3): Financial Distress and Corporate Investment: The Japanese Case in the 9s, ISER discussion paper, Institute of Social and Economic Research, Osaka University. Phillips, P. C. B., and P. Perron (1988): Testing for a Unit Root in Time Series Regression, Biometrika, 75, Sadahiro, A. (5): Sengo Nihon no Makuro Keizai Bunseki. Tokyo: Toyo Keizai, Inc. Silvestrini, A., and D. Veredas (8): Temporal Aggregation of Univariate and Multivariate Time Series Models: A Survey, Journal of Economic Surveys,, Woo, D. (3): In Search of Capital Crunch : Supply Factors behind the Credit Slowdown in Japan, Journal of Money, Credit and Banking, 35,

15 Table 1: P-Values of Phillips-Perron Unit Root Tests SP 1 SP SP 3 SP Q BL π I Intercept Only Intercept & Trend We perform Phillips and Perron s (1988) unit root test. We consider two specifications for the test equation. In the first case, an intercept is included and a trend is not included. In the second case, both intercept and trend are included. Bartlet kernel with the Newey-and-West automatic bandwidth selection is used for each case. The null hypothesis is that there exists a unit root. For stock prices, firm profit, and private investment, the test variable is 1 times year-to-year log difference of the level series. For bank lending, the test variable is changes in 1 times year-to-year log difference of the outstanding of the bank lending. 1

16 Table : Sample Statistics of Differenced Series SP 1 SP SP 3 SP Q BL π I Mean Median Minimum Maximum Std. Dev Skewness Kurtosis p-ks p-ad {SP 1, SP, SP 3 } signify monthly stock prices; SP Q signifies quarterly stock prices; BL signifies bank loans; π signifies firm profit; I signifies private investment. For BL, we take changes in 1 times year-toyear log difference of the outstanding of bank lending. For all other series we take 1 times year-to-year log difference of the level series. Sample period covers months (68 quarters) from 199Q1 through 6Q. p-ks signifies a p-value of the Kolmogorov-Smirnov test for normality. p-ad signifies a p-value of the Anderson-Darling test for normality. 15

17 Table 3: Forecast Error Variance Decomposition of Quarterly VAR() Decomposition of SP Q Decomposition of BL SP Q BL π I SP Q BL π I h = h = h = Decomposition of π Decomposition of I SP Q BL π I SP Q BL π I h = h = h = The model is VAR() of quarterly stock prices SP Q, bank loans BL, firm profit π, and private investment I. In this table we perform the forecast error variance decomposition of each series at prediction horizons h =, 8, 1 quarters. Sample period covers 199Q1-6Q (68 quarters). 16

18 Table : Forecast Error Variance Decomposition of MF-VAR() Decomposition of SP 1 SP 1 SP SP 3 ( 3 j=1 SP j) BL π I h = (.83)...13 h = (.817) h = (.818) Decomposition of SP SP 1 SP SP 3 ( 3 j=1 SP j) BL π I h = (.851) h = (.838) h = (.837) Decomposition of SP 3 SP 1 SP SP 3 ( 3 j=1 SP j) BL π I h = (.85) h = (.8) h = (.83) Decomposition of BL SP 1 SP SP 3 ( 3 j=1 SP j) BL π I h = (.37) h = (.398) h = (.1) Decomposition of π SP 1 SP SP 3 ( 3 j=1 SP j) BL π I h = (.51) h = (.557) h = (.58) Decomposition of I SP 1 SP SP 3 ( 3 j=1 SP j) BL π I h = (.79) h = (.98) h = (.57)...9 The model is MF-VAR() of monthly stock prices {SP 1, SP, SP 3 }, quarterly bank loans BL, firm profit π, and private investment I. In this table we perform the forecast error variance decomposition of each series at prediction horizons h =, 8, 1 quarters. Sample period covers 199Q1-6Q ( months, 68 quarters). 17

19 Figure 1: Stock Prices, Bank Loans, Firm Profit, and Private Investment 5 1 (%) (% Points) Jan9 Jan95 Jan Jan5-1 Q1-9 Q1-95 Q1- Q1-5 (a) Monthly Stock Prices (b) Quarterly Bank Loans 5 (%) (%) -5 - Q1-9 Q1-95 Q1- Q1-5 Q1-9 Q1-95 Q1- Q1-5 (c) Quarterly Firm Profit (d) Quarterly Private Investment For (a) monthly stock prices, (c) quarterly firm profit, and (d) quarterly private investment, we plot 1 times year-to-year log difference of the level series. For (b) quarterly bank loans, we plot changes in 1 times year-to-year log difference of the outstanding of bank loans. Sample period covers months (68 quarters) from January 199 through December 6. For the monthly series, Jan9 signifies January 199. For the quarterly series, Q1-9 signifies the first quarter of 199. Note that y-range differs across panels for visual clarity. 18

20 Figure : Impulse Response Functions Based on Quarterly VAR() BL SP Q. π SP Q 3. I SP Q SP Q BL π BL I BL SP Q π BL π I π SP Q I BL I π I This figure plots impulse response functions based on the quarterly VAR() of stock prices SP Q, bank loans BL, firm profit π, and private investment I. We use the Cholesky decomposition with order SP Q BL π I. Sample period covers 199Q1-6Q. Panel 1, for example, plots the impulse response of SP Q to a 1σ shock in BL, written as BL SP Q, for quarterly horizons h =, 1,..., 1. For each horizon 95% confidence intervals are constructed by parametric bootstrap with 1, replications. 19

21 Figure 3: A. Impulse Response Functions Based on Mixed Frequency VAR() A.1. BL SP 1 A.. BL SP A.3. BL SP A.. π SP 1 A.5. π SP A.6. π SP A.7. I SP 1 A.8. I SP A.9. I SP 3 - Figures 3.A-3.C plot impulse response functions (IRFs) for quarterly horizons h =, 1,..., 1 based on the MF-VAR() of monthly stock prices {SP 1, SP, SP 3 }, quarterly bank loans BL, firm profit π, and private investment I. We use the Cholesky decomposition with order SP 1 SP SP 3 BL π I. Sample period covers 199Q1-6Q. For each horizon h, 95% confidence intervals are constructed by parametric bootstrap with 1, replications. Figure 3.A shows IRFs of stock prices to other variables. Panel A.1, for example, plots the IRF of SP 1 to a 1σ shock in BL, written as BL SP 1.

22 Figure 3: B. Impulse Response Functions Based on Mixed Frequency VAR() B.1. SP 1 BL B.. SP 1 π B.3. SP 1 I B.. SP BL B.5. SP π B.6. SP I B.7. SP 3 BL B.8. SP 3 π B.9. SP 3 I Figures 3.A-3.C plot impulse response functions (IRFs) for quarterly horizons h =, 1,..., 1 based on the MF-VAR() of monthly stock prices {SP 1, SP, SP 3 }, quarterly bank loans BL, firm profit π, and private investment I. We use the Cholesky decomposition with order SP 1 SP SP 3 BL π I. Sample period covers 199Q1-6Q. For each horizon h, 95% confidence intervals are constructed by parametric bootstrap with 1, replications. Figure 3.B shows IRFs of BL, π, and I to stock prices. Panel B.1, for example, plots the IRF of BL to a 1σ shock in SP 1, written as SP 1 BL. 1

23 Figure 3: C. Impulse Response Functions Based on Mixed Frequency VAR() C.1. π BL C.. BL π C.3. BL I C.. I BL C.5. I π C.6. π I Figures 3.A-3.C plot impulse response functions (IRFs) for quarterly horizons h =, 1,..., 1 based on the MF-VAR() of monthly stock prices {SP 1, SP, SP 3 }, quarterly bank loans BL, firm profit π, and private investment I. We use the Cholesky decomposition with order SP 1 SP SP 3 BL π I. Sample period covers 199Q1-6Q. For each horizon h, 95% confidence intervals are constructed by parametric bootstrap with 1, replications. Figure 3.C shows IRFs not involving stock prices. Panel C.1, for example, plots the IRF of BL to a 1σ shock in π, written as π BL.